Most of the mathematical theory that has been developed, with the object of gaining some understanding of the effects of various forces on the genetic structure of populations, is based on the assumption that generations are discrete. One objective of our research has been to examine the extent to which predictions from the theory for populations with discrete generations remain valid when a population with overlapping generations is considered. Some research has been done on theory for both finite and infinite populations with overlapping generations and this line of work will be pursued. We also propose to study genetic theory for populations in which individuals of the same or different species interact with each other. For example, two species might be related as predator and prey or parasite and host. Associated with pure genetic theory is its application to many species, including humans. Statistical problems of interpreting data then arise and it is relevant to examine the logic of data analysis in relation to quantitative genetics. Finally, an attempt will be made to develop a theory of quantitative genetics which integrates multifactorial genetic determination with occurrence of genetically caused variability in viability.